Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(67.6332905120\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.4642000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 8x^{4} + 5x^{3} + 14x^{2} - 9x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 770) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.32077\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.32077 | −0.762545 | −0.381272 | − | 0.924463i | \(-0.624514\pi\) | ||||
−0.381272 | + | 0.924463i | \(0.624514\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.32077 | −0.539201 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.25558 | −0.418526 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.32077 | −0.381272 | ||||||||
\(13\) | 5.34554 | 1.48259 | 0.741293 | − | 0.671182i | \(-0.234213\pi\) | ||||
0.741293 | + | 0.671182i | \(0.234213\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −1.32077 | −0.341020 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.44843 | −1.56397 | −0.781987 | − | 0.623295i | \(-0.785794\pi\) | ||||
−0.781987 | + | 0.623295i | \(0.785794\pi\) | |||||||
\(18\) | −1.25558 | −0.295942 | ||||||||
\(19\) | −6.42752 | −1.47457 | −0.737287 | − | 0.675580i | \(-0.763893\pi\) | ||||
−0.737287 | + | 0.675580i | \(0.763893\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 1.32077 | 0.288215 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.51016 | 1.14895 | 0.574474 | − | 0.818523i | \(-0.305207\pi\) | ||||
0.574474 | + | 0.818523i | \(0.305207\pi\) | |||||||
\(24\) | −1.32077 | −0.269600 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 5.34554 | 1.04835 | ||||||||
\(27\) | 5.62062 | 1.08169 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −8.19519 | −1.52181 | −0.760904 | − | 0.648864i | \(-0.775244\pi\) | ||||
−0.760904 | + | 0.648864i | \(0.775244\pi\) | |||||||
\(30\) | −1.32077 | −0.241138 | ||||||||
\(31\) | 1.77459 | 0.318725 | 0.159363 | − | 0.987220i | \(-0.449056\pi\) | ||||
0.159363 | + | 0.987220i | \(0.449056\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.44843 | −1.10590 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | −1.25558 | −0.209263 | ||||||||
\(37\) | 10.9821 | 1.80544 | 0.902722 | − | 0.430225i | \(-0.141566\pi\) | ||||
0.902722 | + | 0.430225i | \(0.141566\pi\) | |||||||
\(38\) | −6.42752 | −1.04268 | ||||||||
\(39\) | −7.06020 | −1.13054 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 2.08350 | 0.325389 | 0.162694 | − | 0.986677i | \(-0.447982\pi\) | ||||
0.162694 | + | 0.986677i | \(0.447982\pi\) | |||||||
\(42\) | 1.32077 | 0.203799 | ||||||||
\(43\) | −2.71912 | −0.414661 | −0.207331 | − | 0.978271i | \(-0.566478\pi\) | ||||
−0.207331 | + | 0.978271i | \(0.566478\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.25558 | −0.187170 | ||||||||
\(46\) | 5.51016 | 0.812428 | ||||||||
\(47\) | 4.35747 | 0.635603 | 0.317801 | − | 0.948157i | \(-0.397056\pi\) | ||||
0.317801 | + | 0.948157i | \(0.397056\pi\) | |||||||
\(48\) | −1.32077 | −0.190636 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 8.51686 | 1.19260 | ||||||||
\(52\) | 5.34554 | 0.741293 | ||||||||
\(53\) | −8.59127 | −1.18010 | −0.590051 | − | 0.807366i | \(-0.700892\pi\) | ||||
−0.590051 | + | 0.807366i | \(0.700892\pi\) | |||||||
\(54\) | 5.62062 | 0.764870 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 8.48925 | 1.12443 | ||||||||
\(58\) | −8.19519 | −1.07608 | ||||||||
\(59\) | −5.44657 | −0.709083 | −0.354541 | − | 0.935040i | \(-0.615363\pi\) | ||||
−0.354541 | + | 0.935040i | \(0.615363\pi\) | |||||||
\(60\) | −1.32077 | −0.170510 | ||||||||
\(61\) | 13.3987 | 1.71553 | 0.857766 | − | 0.514040i | \(-0.171852\pi\) | ||||
0.857766 | + | 0.514040i | \(0.171852\pi\) | |||||||
\(62\) | 1.77459 | 0.225373 | ||||||||
\(63\) | 1.25558 | 0.158188 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.34554 | 0.663032 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.8106 | −1.32073 | −0.660363 | − | 0.750947i | \(-0.729597\pi\) | ||||
−0.660363 | + | 0.750947i | \(0.729597\pi\) | |||||||
\(68\) | −6.44843 | −0.781987 | ||||||||
\(69\) | −7.27763 | −0.876124 | ||||||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | −11.8156 | −1.40225 | −0.701127 | − | 0.713036i | \(-0.747319\pi\) | ||||
−0.701127 | + | 0.713036i | \(0.747319\pi\) | |||||||
\(72\) | −1.25558 | −0.147971 | ||||||||
\(73\) | −5.54852 | −0.649405 | −0.324702 | − | 0.945816i | \(-0.605264\pi\) | ||||
−0.324702 | + | 0.945816i | \(0.605264\pi\) | |||||||
\(74\) | 10.9821 | 1.27664 | ||||||||
\(75\) | −1.32077 | −0.152509 | ||||||||
\(76\) | −6.42752 | −0.737287 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −7.06020 | −0.799411 | ||||||||
\(79\) | −7.35859 | −0.827906 | −0.413953 | − | 0.910298i | \(-0.635852\pi\) | ||||
−0.413953 | + | 0.910298i | \(0.635852\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −3.65680 | −0.406311 | ||||||||
\(82\) | 2.08350 | 0.230085 | ||||||||
\(83\) | −7.19204 | −0.789429 | −0.394714 | − | 0.918804i | \(-0.629156\pi\) | ||||
−0.394714 | + | 0.918804i | \(0.629156\pi\) | |||||||
\(84\) | 1.32077 | 0.144107 | ||||||||
\(85\) | −6.44843 | −0.699430 | ||||||||
\(86\) | −2.71912 | −0.293210 | ||||||||
\(87\) | 10.8239 | 1.16045 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.39995 | −0.572393 | −0.286197 | − | 0.958171i | \(-0.592391\pi\) | ||||
−0.286197 | + | 0.958171i | \(0.592391\pi\) | |||||||
\(90\) | −1.25558 | −0.132349 | ||||||||
\(91\) | −5.34554 | −0.560364 | ||||||||
\(92\) | 5.51016 | 0.574474 | ||||||||
\(93\) | −2.34381 | −0.243042 | ||||||||
\(94\) | 4.35747 | 0.449439 | ||||||||
\(95\) | −6.42752 | −0.659449 | ||||||||
\(96\) | −1.32077 | −0.134800 | ||||||||
\(97\) | −0.548361 | −0.0556776 | −0.0278388 | − | 0.999612i | \(-0.508863\pi\) | ||||
−0.0278388 | + | 0.999612i | \(0.508863\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 2.44229 | 0.243017 | 0.121509 | − | 0.992590i | \(-0.461227\pi\) | ||||
0.121509 | + | 0.992590i | \(0.461227\pi\) | |||||||
\(102\) | 8.51686 | 0.843295 | ||||||||
\(103\) | 0.630289 | 0.0621042 | 0.0310521 | − | 0.999518i | \(-0.490114\pi\) | ||||
0.0310521 | + | 0.999518i | \(0.490114\pi\) | |||||||
\(104\) | 5.34554 | 0.524173 | ||||||||
\(105\) | 1.32077 | 0.128894 | ||||||||
\(106\) | −8.59127 | −0.834458 | ||||||||
\(107\) | 11.4352 | 1.10549 | 0.552743 | − | 0.833352i | \(-0.313581\pi\) | ||||
0.552743 | + | 0.833352i | \(0.313581\pi\) | |||||||
\(108\) | 5.62062 | 0.540845 | ||||||||
\(109\) | −8.31582 | −0.796512 | −0.398256 | − | 0.917274i | \(-0.630384\pi\) | ||||
−0.398256 | + | 0.917274i | \(0.630384\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −14.5048 | −1.37673 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −20.1474 | −1.89531 | −0.947656 | − | 0.319294i | \(-0.896554\pi\) | ||||
−0.947656 | + | 0.319294i | \(0.896554\pi\) | |||||||
\(114\) | 8.48925 | 0.795091 | ||||||||
\(115\) | 5.51016 | 0.513825 | ||||||||
\(116\) | −8.19519 | −0.760904 | ||||||||
\(117\) | −6.71173 | −0.620500 | ||||||||
\(118\) | −5.44657 | −0.501397 | ||||||||
\(119\) | 6.44843 | 0.591126 | ||||||||
\(120\) | −1.32077 | −0.120569 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 13.3987 | 1.21306 | ||||||||
\(123\) | −2.75182 | −0.248123 | ||||||||
\(124\) | 1.77459 | 0.159363 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 1.25558 | 0.111856 | ||||||||
\(127\) | −11.0010 | −0.976180 | −0.488090 | − | 0.872793i | \(-0.662306\pi\) | ||||
−0.488090 | + | 0.872793i | \(0.662306\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 3.59132 | 0.316198 | ||||||||
\(130\) | 5.34554 | 0.468835 | ||||||||
\(131\) | −18.2978 | −1.59868 | −0.799342 | − | 0.600876i | \(-0.794818\pi\) | ||||
−0.799342 | + | 0.600876i | \(0.794818\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.42752 | 0.557336 | ||||||||
\(134\) | −10.8106 | −0.933894 | ||||||||
\(135\) | 5.62062 | 0.483746 | ||||||||
\(136\) | −6.44843 | −0.552948 | ||||||||
\(137\) | 5.46086 | 0.466552 | 0.233276 | − | 0.972411i | \(-0.425055\pi\) | ||||
0.233276 | + | 0.972411i | \(0.425055\pi\) | |||||||
\(138\) | −7.27763 | −0.619513 | ||||||||
\(139\) | −5.25491 | −0.445716 | −0.222858 | − | 0.974851i | \(-0.571539\pi\) | ||||
−0.222858 | + | 0.974851i | \(0.571539\pi\) | |||||||
\(140\) | −1.00000 | −0.0845154 | ||||||||
\(141\) | −5.75520 | −0.484675 | ||||||||
\(142\) | −11.8156 | −0.991543 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.25558 | −0.104631 | ||||||||
\(145\) | −8.19519 | −0.680574 | ||||||||
\(146\) | −5.54852 | −0.459199 | ||||||||
\(147\) | −1.32077 | −0.108935 | ||||||||
\(148\) | 10.9821 | 0.902722 | ||||||||
\(149\) | 9.21250 | 0.754718 | 0.377359 | − | 0.926067i | \(-0.376832\pi\) | ||||
0.377359 | + | 0.926067i | \(0.376832\pi\) | |||||||
\(150\) | −1.32077 | −0.107840 | ||||||||
\(151\) | 14.2773 | 1.16187 | 0.580936 | − | 0.813949i | \(-0.302686\pi\) | ||||
0.580936 | + | 0.813949i | \(0.302686\pi\) | |||||||
\(152\) | −6.42752 | −0.521340 | ||||||||
\(153\) | 8.09650 | 0.654563 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.77459 | 0.142538 | ||||||||
\(156\) | −7.06020 | −0.565269 | ||||||||
\(157\) | 14.9439 | 1.19265 | 0.596325 | − | 0.802743i | \(-0.296627\pi\) | ||||
0.596325 | + | 0.802743i | \(0.296627\pi\) | |||||||
\(158\) | −7.35859 | −0.585418 | ||||||||
\(159\) | 11.3471 | 0.899880 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −5.51016 | −0.434261 | ||||||||
\(162\) | −3.65680 | −0.287305 | ||||||||
\(163\) | 16.7682 | 1.31339 | 0.656695 | − | 0.754157i | \(-0.271954\pi\) | ||||
0.656695 | + | 0.754157i | \(0.271954\pi\) | |||||||
\(164\) | 2.08350 | 0.162694 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.19204 | −0.558210 | ||||||||
\(167\) | 6.20304 | 0.480006 | 0.240003 | − | 0.970772i | \(-0.422852\pi\) | ||||
0.240003 | + | 0.970772i | \(0.422852\pi\) | |||||||
\(168\) | 1.32077 | 0.101899 | ||||||||
\(169\) | 15.5748 | 1.19806 | ||||||||
\(170\) | −6.44843 | −0.494572 | ||||||||
\(171\) | 8.07024 | 0.617147 | ||||||||
\(172\) | −2.71912 | −0.207331 | ||||||||
\(173\) | −7.35006 | −0.558815 | −0.279407 | − | 0.960173i | \(-0.590138\pi\) | ||||
−0.279407 | + | 0.960173i | \(0.590138\pi\) | |||||||
\(174\) | 10.8239 | 0.820560 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.19364 | 0.540707 | ||||||||
\(178\) | −5.39995 | −0.404743 | ||||||||
\(179\) | −4.40431 | −0.329194 | −0.164597 | − | 0.986361i | \(-0.552632\pi\) | ||||
−0.164597 | + | 0.986361i | \(0.552632\pi\) | |||||||
\(180\) | −1.25558 | −0.0935852 | ||||||||
\(181\) | −11.0910 | −0.824387 | −0.412193 | − | 0.911096i | \(-0.635237\pi\) | ||||
−0.412193 | + | 0.911096i | \(0.635237\pi\) | |||||||
\(182\) | −5.34554 | −0.396238 | ||||||||
\(183\) | −17.6966 | −1.30817 | ||||||||
\(184\) | 5.51016 | 0.406214 | ||||||||
\(185\) | 10.9821 | 0.807419 | ||||||||
\(186\) | −2.34381 | −0.171857 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 4.35747 | 0.317801 | ||||||||
\(189\) | −5.62062 | −0.408840 | ||||||||
\(190\) | −6.42752 | −0.466301 | ||||||||
\(191\) | −14.3562 | −1.03878 | −0.519388 | − | 0.854538i | \(-0.673840\pi\) | ||||
−0.519388 | + | 0.854538i | \(0.673840\pi\) | |||||||
\(192\) | −1.32077 | −0.0953181 | ||||||||
\(193\) | 8.48187 | 0.610538 | 0.305269 | − | 0.952266i | \(-0.401254\pi\) | ||||
0.305269 | + | 0.952266i | \(0.401254\pi\) | |||||||
\(194\) | −0.548361 | −0.0393700 | ||||||||
\(195\) | −7.06020 | −0.505592 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −4.97357 | −0.354352 | −0.177176 | − | 0.984179i | \(-0.556696\pi\) | ||||
−0.177176 | + | 0.984179i | \(0.556696\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.6336 | −1.60445 | −0.802227 | − | 0.597018i | \(-0.796352\pi\) | ||||
−0.802227 | + | 0.597018i | \(0.796352\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 14.2783 | 1.00711 | ||||||||
\(202\) | 2.44229 | 0.171839 | ||||||||
\(203\) | 8.19519 | 0.575190 | ||||||||
\(204\) | 8.51686 | 0.596300 | ||||||||
\(205\) | 2.08350 | 0.145518 | ||||||||
\(206\) | 0.630289 | 0.0439143 | ||||||||
\(207\) | −6.91843 | −0.480864 | ||||||||
\(208\) | 5.34554 | 0.370646 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1.32077 | 0.0911415 | ||||||||
\(211\) | −3.78425 | −0.260519 | −0.130259 | − | 0.991480i | \(-0.541581\pi\) | ||||
−0.130259 | + | 0.991480i | \(0.541581\pi\) | |||||||
\(212\) | −8.59127 | −0.590051 | ||||||||
\(213\) | 15.6056 | 1.06928 | ||||||||
\(214\) | 11.4352 | 0.781697 | ||||||||
\(215\) | −2.71912 | −0.185442 | ||||||||
\(216\) | 5.62062 | 0.382435 | ||||||||
\(217\) | −1.77459 | −0.120467 | ||||||||
\(218\) | −8.31582 | −0.563219 | ||||||||
\(219\) | 7.32830 | 0.495200 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −34.4703 | −2.31872 | ||||||||
\(222\) | −14.5048 | −0.973496 | ||||||||
\(223\) | 22.5140 | 1.50765 | 0.753824 | − | 0.657077i | \(-0.228207\pi\) | ||||
0.753824 | + | 0.657077i | \(0.228207\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −1.25558 | −0.0837051 | ||||||||
\(226\) | −20.1474 | −1.34019 | ||||||||
\(227\) | −10.8997 | −0.723439 | −0.361719 | − | 0.932287i | \(-0.617810\pi\) | ||||
−0.361719 | + | 0.932287i | \(0.617810\pi\) | |||||||
\(228\) | 8.48925 | 0.562214 | ||||||||
\(229\) | −3.17445 | −0.209773 | −0.104887 | − | 0.994484i | \(-0.533448\pi\) | ||||
−0.104887 | + | 0.994484i | \(0.533448\pi\) | |||||||
\(230\) | 5.51016 | 0.363329 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.19519 | −0.538041 | ||||||||
\(233\) | −25.6323 | −1.67923 | −0.839614 | − | 0.543184i | \(-0.817219\pi\) | ||||
−0.839614 | + | 0.543184i | \(0.817219\pi\) | |||||||
\(234\) | −6.71173 | −0.438760 | ||||||||
\(235\) | 4.35747 | 0.284250 | ||||||||
\(236\) | −5.44657 | −0.354541 | ||||||||
\(237\) | 9.71897 | 0.631315 | ||||||||
\(238\) | 6.44843 | 0.417989 | ||||||||
\(239\) | −17.5664 | −1.13628 | −0.568139 | − | 0.822932i | \(-0.692337\pi\) | ||||
−0.568139 | + | 0.822932i | \(0.692337\pi\) | |||||||
\(240\) | −1.32077 | −0.0852551 | ||||||||
\(241\) | 5.63187 | 0.362781 | 0.181390 | − | 0.983411i | \(-0.441940\pi\) | ||||
0.181390 | + | 0.983411i | \(0.441940\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.0321 | −0.771859 | ||||||||
\(244\) | 13.3987 | 0.857766 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | −2.75182 | −0.175450 | ||||||||
\(247\) | −34.3585 | −2.18618 | ||||||||
\(248\) | 1.77459 | 0.112686 | ||||||||
\(249\) | 9.49900 | 0.601975 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 14.3083 | 0.903130 | 0.451565 | − | 0.892238i | \(-0.350866\pi\) | ||||
0.451565 | + | 0.892238i | \(0.350866\pi\) | |||||||
\(252\) | 1.25558 | 0.0790939 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −11.0010 | −0.690263 | ||||||||
\(255\) | 8.51686 | 0.533347 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −7.69294 | −0.479872 | −0.239936 | − | 0.970789i | \(-0.577126\pi\) | ||||
−0.239936 | + | 0.970789i | \(0.577126\pi\) | |||||||
\(258\) | 3.59132 | 0.223586 | ||||||||
\(259\) | −10.9821 | −0.682393 | ||||||||
\(260\) | 5.34554 | 0.331516 | ||||||||
\(261\) | 10.2897 | 0.636916 | ||||||||
\(262\) | −18.2978 | −1.13044 | ||||||||
\(263\) | −6.81613 | −0.420300 | −0.210150 | − | 0.977669i | \(-0.567395\pi\) | ||||
−0.210150 | + | 0.977669i | \(0.567395\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.59127 | −0.527758 | ||||||||
\(266\) | 6.42752 | 0.394096 | ||||||||
\(267\) | 7.13207 | 0.436475 | ||||||||
\(268\) | −10.8106 | −0.660363 | ||||||||
\(269\) | 3.79822 | 0.231581 | 0.115791 | − | 0.993274i | \(-0.463060\pi\) | ||||
0.115791 | + | 0.993274i | \(0.463060\pi\) | |||||||
\(270\) | 5.62062 | 0.342060 | ||||||||
\(271\) | 2.35406 | 0.142999 | 0.0714996 | − | 0.997441i | \(-0.477222\pi\) | ||||
0.0714996 | + | 0.997441i | \(0.477222\pi\) | |||||||
\(272\) | −6.44843 | −0.390993 | ||||||||
\(273\) | 7.06020 | 0.427303 | ||||||||
\(274\) | 5.46086 | 0.329902 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −7.27763 | −0.438062 | ||||||||
\(277\) | −17.4409 | −1.04792 | −0.523962 | − | 0.851742i | \(-0.675547\pi\) | ||||
−0.523962 | + | 0.851742i | \(0.675547\pi\) | |||||||
\(278\) | −5.25491 | −0.315169 | ||||||||
\(279\) | −2.22813 | −0.133395 | ||||||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | −22.6310 | −1.35005 | −0.675027 | − | 0.737793i | \(-0.735868\pi\) | ||||
−0.675027 | + | 0.737793i | \(0.735868\pi\) | |||||||
\(282\) | −5.75520 | −0.342717 | ||||||||
\(283\) | −27.0596 | −1.60852 | −0.804262 | − | 0.594274i | \(-0.797439\pi\) | ||||
−0.804262 | + | 0.594274i | \(0.797439\pi\) | |||||||
\(284\) | −11.8156 | −0.701127 | ||||||||
\(285\) | 8.48925 | 0.502860 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.08350 | −0.122985 | ||||||||
\(288\) | −1.25558 | −0.0739856 | ||||||||
\(289\) | 24.5822 | 1.44601 | ||||||||
\(290\) | −8.19519 | −0.481238 | ||||||||
\(291\) | 0.724257 | 0.0424567 | ||||||||
\(292\) | −5.54852 | −0.324702 | ||||||||
\(293\) | −20.1958 | −1.17985 | −0.589926 | − | 0.807458i | \(-0.700843\pi\) | ||||
−0.589926 | + | 0.807458i | \(0.700843\pi\) | |||||||
\(294\) | −1.32077 | −0.0770286 | ||||||||
\(295\) | −5.44657 | −0.317111 | ||||||||
\(296\) | 10.9821 | 0.638321 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 9.21250 | 0.533666 | ||||||||
\(299\) | 29.4547 | 1.70341 | ||||||||
\(300\) | −1.32077 | −0.0762545 | ||||||||
\(301\) | 2.71912 | 0.156727 | ||||||||
\(302\) | 14.2773 | 0.821568 | ||||||||
\(303\) | −3.22570 | −0.185311 | ||||||||
\(304\) | −6.42752 | −0.368643 | ||||||||
\(305\) | 13.3987 | 0.767209 | ||||||||
\(306\) | 8.09650 | 0.462846 | ||||||||
\(307\) | 24.4128 | 1.39331 | 0.696656 | − | 0.717405i | \(-0.254670\pi\) | ||||
0.696656 | + | 0.717405i | \(0.254670\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.832464 | −0.0473572 | ||||||||
\(310\) | 1.77459 | 0.100790 | ||||||||
\(311\) | 25.2667 | 1.43274 | 0.716371 | − | 0.697720i | \(-0.245802\pi\) | ||||
0.716371 | + | 0.697720i | \(0.245802\pi\) | |||||||
\(312\) | −7.06020 | −0.399705 | ||||||||
\(313\) | −18.1747 | −1.02729 | −0.513647 | − | 0.858002i | \(-0.671706\pi\) | ||||
−0.513647 | + | 0.858002i | \(0.671706\pi\) | |||||||
\(314\) | 14.9439 | 0.843331 | ||||||||
\(315\) | 1.25558 | 0.0707437 | ||||||||
\(316\) | −7.35859 | −0.413953 | ||||||||
\(317\) | 10.6739 | 0.599506 | 0.299753 | − | 0.954017i | \(-0.403096\pi\) | ||||
0.299753 | + | 0.954017i | \(0.403096\pi\) | |||||||
\(318\) | 11.3471 | 0.636312 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −15.1033 | −0.842983 | ||||||||
\(322\) | −5.51016 | −0.307069 | ||||||||
\(323\) | 41.4474 | 2.30619 | ||||||||
\(324\) | −3.65680 | −0.203155 | ||||||||
\(325\) | 5.34554 | 0.296517 | ||||||||
\(326\) | 16.7682 | 0.928707 | ||||||||
\(327\) | 10.9833 | 0.607376 | ||||||||
\(328\) | 2.08350 | 0.115042 | ||||||||
\(329\) | −4.35747 | −0.240235 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.75660 | −0.536271 | −0.268136 | − | 0.963381i | \(-0.586408\pi\) | ||||
−0.268136 | + | 0.963381i | \(0.586408\pi\) | |||||||
\(332\) | −7.19204 | −0.394714 | ||||||||
\(333\) | −13.7888 | −0.755624 | ||||||||
\(334\) | 6.20304 | 0.339415 | ||||||||
\(335\) | −10.8106 | −0.590646 | ||||||||
\(336\) | 1.32077 | 0.0720537 | ||||||||
\(337\) | 10.1462 | 0.552699 | 0.276350 | − | 0.961057i | \(-0.410875\pi\) | ||||
0.276350 | + | 0.961057i | \(0.410875\pi\) | |||||||
\(338\) | 15.5748 | 0.847155 | ||||||||
\(339\) | 26.6101 | 1.44526 | ||||||||
\(340\) | −6.44843 | −0.349715 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 8.07024 | 0.436389 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −2.71912 | −0.146605 | ||||||||
\(345\) | −7.27763 | −0.391814 | ||||||||
\(346\) | −7.35006 | −0.395142 | ||||||||
\(347\) | −21.1756 | −1.13677 | −0.568383 | − | 0.822764i | \(-0.692431\pi\) | ||||
−0.568383 | + | 0.822764i | \(0.692431\pi\) | |||||||
\(348\) | 10.8239 | 0.580224 | ||||||||
\(349\) | −4.58943 | −0.245667 | −0.122833 | − | 0.992427i | \(-0.539198\pi\) | ||||
−0.122833 | + | 0.992427i | \(0.539198\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | 30.0452 | 1.60370 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 32.2094 | 1.71433 | 0.857166 | − | 0.515040i | \(-0.172223\pi\) | ||||
0.857166 | + | 0.515040i | \(0.172223\pi\) | |||||||
\(354\) | 7.19364 | 0.382338 | ||||||||
\(355\) | −11.8156 | −0.627107 | ||||||||
\(356\) | −5.39995 | −0.286197 | ||||||||
\(357\) | −8.51686 | −0.450760 | ||||||||
\(358\) | −4.40431 | −0.232775 | ||||||||
\(359\) | −6.54031 | −0.345184 | −0.172592 | − | 0.984993i | \(-0.555214\pi\) | ||||
−0.172592 | + | 0.984993i | \(0.555214\pi\) | |||||||
\(360\) | −1.25558 | −0.0661747 | ||||||||
\(361\) | 22.3130 | 1.17437 | ||||||||
\(362\) | −11.0910 | −0.582930 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.34554 | −0.280182 | ||||||||
\(365\) | −5.54852 | −0.290423 | ||||||||
\(366\) | −17.6966 | −0.925016 | ||||||||
\(367\) | −2.98556 | −0.155845 | −0.0779225 | − | 0.996959i | \(-0.524829\pi\) | ||||
−0.0779225 | + | 0.996959i | \(0.524829\pi\) | |||||||
\(368\) | 5.51016 | 0.287237 | ||||||||
\(369\) | −2.61600 | −0.136183 | ||||||||
\(370\) | 10.9821 | 0.570931 | ||||||||
\(371\) | 8.59127 | 0.446037 | ||||||||
\(372\) | −2.34381 | −0.121521 | ||||||||
\(373\) | −16.8471 | −0.872311 | −0.436155 | − | 0.899871i | \(-0.643660\pi\) | ||||
−0.436155 | + | 0.899871i | \(0.643660\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.32077 | −0.0682041 | ||||||||
\(376\) | 4.35747 | 0.224719 | ||||||||
\(377\) | −43.8077 | −2.25621 | ||||||||
\(378\) | −5.62062 | −0.289094 | ||||||||
\(379\) | −27.4781 | −1.41145 | −0.705727 | − | 0.708484i | \(-0.749380\pi\) | ||||
−0.705727 | + | 0.708484i | \(0.749380\pi\) | |||||||
\(380\) | −6.42752 | −0.329725 | ||||||||
\(381\) | 14.5297 | 0.744381 | ||||||||
\(382\) | −14.3562 | −0.734526 | ||||||||
\(383\) | −31.3930 | −1.60411 | −0.802055 | − | 0.597251i | \(-0.796260\pi\) | ||||
−0.802055 | + | 0.597251i | \(0.796260\pi\) | |||||||
\(384\) | −1.32077 | −0.0674001 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.48187 | 0.431716 | ||||||||
\(387\) | 3.41406 | 0.173546 | ||||||||
\(388\) | −0.548361 | −0.0278388 | ||||||||
\(389\) | −0.115199 | −0.00584080 | −0.00292040 | − | 0.999996i | \(-0.500930\pi\) | ||||
−0.00292040 | + | 0.999996i | \(0.500930\pi\) | |||||||
\(390\) | −7.06020 | −0.357507 | ||||||||
\(391\) | −35.5318 | −1.79692 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 24.1671 | 1.21907 | ||||||||
\(394\) | −4.97357 | −0.250565 | ||||||||
\(395\) | −7.35859 | −0.370251 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.2744 | −0.917165 | −0.458583 | − | 0.888652i | \(-0.651643\pi\) | ||||
−0.458583 | + | 0.888652i | \(0.651643\pi\) | |||||||
\(398\) | −22.6336 | −1.13452 | ||||||||
\(399\) | −8.48925 | −0.424994 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 30.0646 | 1.50136 | 0.750678 | − | 0.660668i | \(-0.229727\pi\) | ||||
0.750678 | + | 0.660668i | \(0.229727\pi\) | |||||||
\(402\) | 14.2783 | 0.712136 | ||||||||
\(403\) | 9.48612 | 0.472537 | ||||||||
\(404\) | 2.44229 | 0.121509 | ||||||||
\(405\) | −3.65680 | −0.181708 | ||||||||
\(406\) | 8.19519 | 0.406720 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 8.51686 | 0.421648 | ||||||||
\(409\) | 29.2637 | 1.44700 | 0.723499 | − | 0.690326i | \(-0.242533\pi\) | ||||
0.723499 | + | 0.690326i | \(0.242533\pi\) | |||||||
\(410\) | 2.08350 | 0.102897 | ||||||||
\(411\) | −7.21252 | −0.355767 | ||||||||
\(412\) | 0.630289 | 0.0310521 | ||||||||
\(413\) | 5.44657 | 0.268008 | ||||||||
\(414\) | −6.91843 | −0.340022 | ||||||||
\(415\) | −7.19204 | −0.353043 | ||||||||
\(416\) | 5.34554 | 0.262086 | ||||||||
\(417\) | 6.94051 | 0.339878 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.3655 | −0.848362 | −0.424181 | − | 0.905577i | \(-0.639438\pi\) | ||||
−0.424181 | + | 0.905577i | \(0.639438\pi\) | |||||||
\(420\) | 1.32077 | 0.0644468 | ||||||||
\(421\) | 8.29303 | 0.404177 | 0.202089 | − | 0.979367i | \(-0.435227\pi\) | ||||
0.202089 | + | 0.979367i | \(0.435227\pi\) | |||||||
\(422\) | −3.78425 | −0.184214 | ||||||||
\(423\) | −5.47114 | −0.266016 | ||||||||
\(424\) | −8.59127 | −0.417229 | ||||||||
\(425\) | −6.44843 | −0.312795 | ||||||||
\(426\) | 15.6056 | 0.756096 | ||||||||
\(427\) | −13.3987 | −0.648410 | ||||||||
\(428\) | 11.4352 | 0.552743 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.71912 | −0.131127 | ||||||||
\(431\) | 13.3393 | 0.642530 | 0.321265 | − | 0.946989i | \(-0.395892\pi\) | ||||
0.321265 | + | 0.946989i | \(0.395892\pi\) | |||||||
\(432\) | 5.62062 | 0.270422 | ||||||||
\(433\) | −14.8300 | −0.712685 | −0.356342 | − | 0.934355i | \(-0.615976\pi\) | ||||
−0.356342 | + | 0.934355i | \(0.615976\pi\) | |||||||
\(434\) | −1.77459 | −0.0851829 | ||||||||
\(435\) | 10.8239 | 0.518968 | ||||||||
\(436\) | −8.31582 | −0.398256 | ||||||||
\(437\) | −35.4166 | −1.69421 | ||||||||
\(438\) | 7.32830 | 0.350160 | ||||||||
\(439\) | −6.08156 | −0.290257 | −0.145128 | − | 0.989413i | \(-0.546360\pi\) | ||||
−0.145128 | + | 0.989413i | \(0.546360\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.25558 | −0.0597894 | ||||||||
\(442\) | −34.4703 | −1.63959 | ||||||||
\(443\) | −19.8590 | −0.943530 | −0.471765 | − | 0.881724i | \(-0.656383\pi\) | ||||
−0.471765 | + | 0.881724i | \(0.656383\pi\) | |||||||
\(444\) | −14.5048 | −0.688366 | ||||||||
\(445\) | −5.39995 | −0.255982 | ||||||||
\(446\) | 22.5140 | 1.06607 | ||||||||
\(447\) | −12.1676 | −0.575506 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 0.806539 | 0.0380629 | 0.0190315 | − | 0.999819i | \(-0.493942\pi\) | ||||
0.0190315 | + | 0.999819i | \(0.493942\pi\) | |||||||
\(450\) | −1.25558 | −0.0591885 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −20.1474 | −0.947656 | ||||||||
\(453\) | −18.8570 | −0.885980 | ||||||||
\(454\) | −10.8997 | −0.511548 | ||||||||
\(455\) | −5.34554 | −0.250603 | ||||||||
\(456\) | 8.48925 | 0.397545 | ||||||||
\(457\) | −29.9349 | −1.40030 | −0.700149 | − | 0.713997i | \(-0.746883\pi\) | ||||
−0.700149 | + | 0.713997i | \(0.746883\pi\) | |||||||
\(458\) | −3.17445 | −0.148332 | ||||||||
\(459\) | −36.2442 | −1.69173 | ||||||||
\(460\) | 5.51016 | 0.256912 | ||||||||
\(461\) | 33.4831 | 1.55946 | 0.779732 | − | 0.626114i | \(-0.215355\pi\) | ||||
0.779732 | + | 0.626114i | \(0.215355\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.7511 | −1.38265 | −0.691324 | − | 0.722545i | \(-0.742972\pi\) | ||||
−0.691324 | + | 0.722545i | \(0.742972\pi\) | |||||||
\(464\) | −8.19519 | −0.380452 | ||||||||
\(465\) | −2.34381 | −0.108692 | ||||||||
\(466\) | −25.6323 | −1.18739 | ||||||||
\(467\) | −6.65053 | −0.307750 | −0.153875 | − | 0.988090i | \(-0.549175\pi\) | ||||
−0.153875 | + | 0.988090i | \(0.549175\pi\) | |||||||
\(468\) | −6.71173 | −0.310250 | ||||||||
\(469\) | 10.8106 | 0.499187 | ||||||||
\(470\) | 4.35747 | 0.200995 | ||||||||
\(471\) | −19.7373 | −0.909449 | ||||||||
\(472\) | −5.44657 | −0.250699 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 9.71897 | 0.446407 | ||||||||
\(475\) | −6.42752 | −0.294915 | ||||||||
\(476\) | 6.44843 | 0.295563 | ||||||||
\(477\) | 10.7870 | 0.493903 | ||||||||
\(478\) | −17.5664 | −0.803470 | ||||||||
\(479\) | −17.9277 | −0.819137 | −0.409569 | − | 0.912279i | \(-0.634321\pi\) | ||||
−0.409569 | + | 0.912279i | \(0.634321\pi\) | |||||||
\(480\) | −1.32077 | −0.0602845 | ||||||||
\(481\) | 58.7051 | 2.67672 | ||||||||
\(482\) | 5.63187 | 0.256525 | ||||||||
\(483\) | 7.27763 | 0.331144 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.548361 | −0.0248998 | ||||||||
\(486\) | −12.0321 | −0.545787 | ||||||||
\(487\) | 37.2239 | 1.68677 | 0.843387 | − | 0.537307i | \(-0.180558\pi\) | ||||
0.843387 | + | 0.537307i | \(0.180558\pi\) | |||||||
\(488\) | 13.3987 | 0.606532 | ||||||||
\(489\) | −22.1469 | −1.00152 | ||||||||
\(490\) | 1.00000 | 0.0451754 | ||||||||
\(491\) | −21.7165 | −0.980051 | −0.490026 | − | 0.871708i | \(-0.663013\pi\) | ||||
−0.490026 | + | 0.871708i | \(0.663013\pi\) | |||||||
\(492\) | −2.75182 | −0.124062 | ||||||||
\(493\) | 52.8461 | 2.38007 | ||||||||
\(494\) | −34.3585 | −1.54586 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.77459 | 0.0796813 | ||||||||
\(497\) | 11.8156 | 0.530002 | ||||||||
\(498\) | 9.49900 | 0.425660 | ||||||||
\(499\) | −15.7823 | −0.706515 | −0.353257 | − | 0.935526i | \(-0.614926\pi\) | ||||
−0.353257 | + | 0.935526i | \(0.614926\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −8.19277 | −0.366026 | ||||||||
\(502\) | 14.3083 | 0.638610 | ||||||||
\(503\) | −8.96024 | −0.399517 | −0.199759 | − | 0.979845i | \(-0.564016\pi\) | ||||
−0.199759 | + | 0.979845i | \(0.564016\pi\) | |||||||
\(504\) | 1.25558 | 0.0559278 | ||||||||
\(505\) | 2.44229 | 0.108681 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −20.5706 | −0.913573 | ||||||||
\(508\) | −11.0010 | −0.488090 | ||||||||
\(509\) | 43.5620 | 1.93085 | 0.965426 | − | 0.260678i | \(-0.0839461\pi\) | ||||
0.965426 | + | 0.260678i | \(0.0839461\pi\) | |||||||
\(510\) | 8.51686 | 0.377133 | ||||||||
\(511\) | 5.54852 | 0.245452 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −36.1266 | −1.59503 | ||||||||
\(514\) | −7.69294 | −0.339321 | ||||||||
\(515\) | 0.630289 | 0.0277738 | ||||||||
\(516\) | 3.59132 | 0.158099 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −10.9821 | −0.482525 | ||||||||
\(519\) | 9.70771 | 0.426121 | ||||||||
\(520\) | 5.34554 | 0.234417 | ||||||||
\(521\) | 0.872633 | 0.0382307 | 0.0191154 | − | 0.999817i | \(-0.493915\pi\) | ||||
0.0191154 | + | 0.999817i | \(0.493915\pi\) | |||||||
\(522\) | 10.2897 | 0.450368 | ||||||||
\(523\) | −22.4315 | −0.980860 | −0.490430 | − | 0.871481i | \(-0.663160\pi\) | ||||
−0.490430 | + | 0.871481i | \(0.663160\pi\) | |||||||
\(524\) | −18.2978 | −0.799342 | ||||||||
\(525\) | 1.32077 | 0.0576430 | ||||||||
\(526\) | −6.81613 | −0.297197 | ||||||||
\(527\) | −11.4433 | −0.498478 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.36183 | 0.320080 | ||||||||
\(530\) | −8.59127 | −0.373181 | ||||||||
\(531\) | 6.83858 | 0.296769 | ||||||||
\(532\) | 6.42752 | 0.278668 | ||||||||
\(533\) | 11.1374 | 0.482416 | ||||||||
\(534\) | 7.13207 | 0.308635 | ||||||||
\(535\) | 11.4352 | 0.494389 | ||||||||
\(536\) | −10.8106 | −0.466947 | ||||||||
\(537\) | 5.81707 | 0.251025 | ||||||||
\(538\) | 3.79822 | 0.163753 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 5.62062 | 0.241873 | ||||||||
\(541\) | −10.0432 | −0.431793 | −0.215896 | − | 0.976416i | \(-0.569267\pi\) | ||||
−0.215896 | + | 0.976416i | \(0.569267\pi\) | |||||||
\(542\) | 2.35406 | 0.101116 | ||||||||
\(543\) | 14.6486 | 0.628632 | ||||||||
\(544\) | −6.44843 | −0.276474 | ||||||||
\(545\) | −8.31582 | −0.356211 | ||||||||
\(546\) | 7.06020 | 0.302149 | ||||||||
\(547\) | −15.3645 | −0.656937 | −0.328469 | − | 0.944515i | \(-0.606533\pi\) | ||||
−0.328469 | + | 0.944515i | \(0.606533\pi\) | |||||||
\(548\) | 5.46086 | 0.233276 | ||||||||
\(549\) | −16.8231 | −0.717994 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 52.6747 | 2.24402 | ||||||||
\(552\) | −7.27763 | −0.309756 | ||||||||
\(553\) | 7.35859 | 0.312919 | ||||||||
\(554\) | −17.4409 | −0.740994 | ||||||||
\(555\) | −14.5048 | −0.615693 | ||||||||
\(556\) | −5.25491 | −0.222858 | ||||||||
\(557\) | −45.8170 | −1.94133 | −0.970665 | − | 0.240437i | \(-0.922709\pi\) | ||||
−0.970665 | + | 0.240437i | \(0.922709\pi\) | |||||||
\(558\) | −2.22813 | −0.0943243 | ||||||||
\(559\) | −14.5351 | −0.614770 | ||||||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −22.6310 | −0.954632 | ||||||||
\(563\) | −17.1178 | −0.721429 | −0.360714 | − | 0.932676i | \(-0.617467\pi\) | ||||
−0.360714 | + | 0.932676i | \(0.617467\pi\) | |||||||
\(564\) | −5.75520 | −0.242338 | ||||||||
\(565\) | −20.1474 | −0.847609 | ||||||||
\(566\) | −27.0596 | −1.13740 | ||||||||
\(567\) | 3.65680 | 0.153571 | ||||||||
\(568\) | −11.8156 | −0.495772 | ||||||||
\(569\) | 18.0666 | 0.757389 | 0.378695 | − | 0.925522i | \(-0.376373\pi\) | ||||
0.378695 | + | 0.925522i | \(0.376373\pi\) | |||||||
\(570\) | 8.48925 | 0.355575 | ||||||||
\(571\) | 13.8533 | 0.579743 | 0.289872 | − | 0.957066i | \(-0.406387\pi\) | ||||
0.289872 | + | 0.957066i | \(0.406387\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.9612 | 0.792114 | ||||||||
\(574\) | −2.08350 | −0.0869638 | ||||||||
\(575\) | 5.51016 | 0.229789 | ||||||||
\(576\) | −1.25558 | −0.0523157 | ||||||||
\(577\) | 39.1469 | 1.62971 | 0.814854 | − | 0.579667i | \(-0.196817\pi\) | ||||
0.814854 | + | 0.579667i | \(0.196817\pi\) | |||||||
\(578\) | 24.5822 | 1.02249 | ||||||||
\(579\) | −11.2026 | −0.465563 | ||||||||
\(580\) | −8.19519 | −0.340287 | ||||||||
\(581\) | 7.19204 | 0.298376 | ||||||||
\(582\) | 0.724257 | 0.0300214 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −5.54852 | −0.229599 | ||||||||
\(585\) | −6.71173 | −0.277496 | ||||||||
\(586\) | −20.1958 | −0.834281 | ||||||||
\(587\) | −25.3734 | −1.04727 | −0.523637 | − | 0.851942i | \(-0.675425\pi\) | ||||
−0.523637 | + | 0.851942i | \(0.675425\pi\) | |||||||
\(588\) | −1.32077 | −0.0544675 | ||||||||
\(589\) | −11.4062 | −0.469984 | ||||||||
\(590\) | −5.44657 | −0.224232 | ||||||||
\(591\) | 6.56892 | 0.270209 | ||||||||
\(592\) | 10.9821 | 0.451361 | ||||||||
\(593\) | 24.5601 | 1.00856 | 0.504280 | − | 0.863540i | \(-0.331758\pi\) | ||||
0.504280 | + | 0.863540i | \(0.331758\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.44843 | 0.264360 | ||||||||
\(596\) | 9.21250 | 0.377359 | ||||||||
\(597\) | 29.8937 | 1.22347 | ||||||||
\(598\) | 29.4547 | 1.20449 | ||||||||
\(599\) | −35.4719 | −1.44934 | −0.724672 | − | 0.689094i | \(-0.758009\pi\) | ||||
−0.724672 | + | 0.689094i | \(0.758009\pi\) | |||||||
\(600\) | −1.32077 | −0.0539201 | ||||||||
\(601\) | −14.7392 | −0.601223 | −0.300611 | − | 0.953747i | \(-0.597191\pi\) | ||||
−0.300611 | + | 0.953747i | \(0.597191\pi\) | |||||||
\(602\) | 2.71912 | 0.110823 | ||||||||
\(603\) | 13.5735 | 0.552757 | ||||||||
\(604\) | 14.2773 | 0.580936 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.22570 | −0.131035 | ||||||||
\(607\) | 6.09924 | 0.247560 | 0.123780 | − | 0.992310i | \(-0.460498\pi\) | ||||
0.123780 | + | 0.992310i | \(0.460498\pi\) | |||||||
\(608\) | −6.42752 | −0.260670 | ||||||||
\(609\) | −10.8239 | −0.438608 | ||||||||
\(610\) | 13.3987 | 0.542499 | ||||||||
\(611\) | 23.2930 | 0.942335 | ||||||||
\(612\) | 8.09650 | 0.327281 | ||||||||
\(613\) | 18.0889 | 0.730604 | 0.365302 | − | 0.930889i | \(-0.380966\pi\) | ||||
0.365302 | + | 0.930889i | \(0.380966\pi\) | |||||||
\(614\) | 24.4128 | 0.985221 | ||||||||
\(615\) | −2.75182 | −0.110964 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.9814 | 0.643386 | 0.321693 | − | 0.946844i | \(-0.395748\pi\) | ||||
0.321693 | + | 0.946844i | \(0.395748\pi\) | |||||||
\(618\) | −0.832464 | −0.0334866 | ||||||||
\(619\) | 5.20453 | 0.209188 | 0.104594 | − | 0.994515i | \(-0.466646\pi\) | ||||
0.104594 | + | 0.994515i | \(0.466646\pi\) | |||||||
\(620\) | 1.77459 | 0.0712691 | ||||||||
\(621\) | 30.9705 | 1.24280 | ||||||||
\(622\) | 25.2667 | 1.01310 | ||||||||
\(623\) | 5.39995 | 0.216344 | ||||||||
\(624\) | −7.06020 | −0.282634 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −18.1747 | −0.726407 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14.9439 | 0.596325 | ||||||||
\(629\) | −70.8172 | −2.82367 | ||||||||
\(630\) | 1.25558 | 0.0500234 | ||||||||
\(631\) | −34.2712 | −1.36432 | −0.682158 | − | 0.731204i | \(-0.738959\pi\) | ||||
−0.682158 | + | 0.731204i | \(0.738959\pi\) | |||||||
\(632\) | −7.35859 | −0.292709 | ||||||||
\(633\) | 4.99811 | 0.198657 | ||||||||
\(634\) | 10.6739 | 0.423915 | ||||||||
\(635\) | −11.0010 | −0.436561 | ||||||||
\(636\) | 11.3471 | 0.449940 | ||||||||
\(637\) | 5.34554 | 0.211798 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.8354 | 0.586879 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 38.3894 | 1.51629 | 0.758145 | − | 0.652086i | \(-0.226106\pi\) | ||||
0.758145 | + | 0.652086i | \(0.226106\pi\) | |||||||
\(642\) | −15.1033 | −0.596079 | ||||||||
\(643\) | 4.86445 | 0.191835 | 0.0959177 | − | 0.995389i | \(-0.469421\pi\) | ||||
0.0959177 | + | 0.995389i | \(0.469421\pi\) | |||||||
\(644\) | −5.51016 | −0.217131 | ||||||||
\(645\) | 3.59132 | 0.141408 | ||||||||
\(646\) | 41.4474 | 1.63073 | ||||||||
\(647\) | 13.6415 | 0.536303 | 0.268151 | − | 0.963377i | \(-0.413587\pi\) | ||||
0.268151 | + | 0.963377i | \(0.413587\pi\) | |||||||
\(648\) | −3.65680 | −0.143653 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 5.34554 | 0.209669 | ||||||||
\(651\) | 2.34381 | 0.0918613 | ||||||||
\(652\) | 16.7682 | 0.656695 | ||||||||
\(653\) | 21.3235 | 0.834453 | 0.417226 | − | 0.908803i | \(-0.363002\pi\) | ||||
0.417226 | + | 0.908803i | \(0.363002\pi\) | |||||||
\(654\) | 10.9833 | 0.429479 | ||||||||
\(655\) | −18.2978 | −0.714953 | ||||||||
\(656\) | 2.08350 | 0.0813472 | ||||||||
\(657\) | 6.96659 | 0.271793 | ||||||||
\(658\) | −4.35747 | −0.169872 | ||||||||
\(659\) | −12.6150 | −0.491409 | −0.245704 | − | 0.969345i | \(-0.579019\pi\) | ||||
−0.245704 | + | 0.969345i | \(0.579019\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32.2901 | 1.25594 | 0.627969 | − | 0.778238i | \(-0.283886\pi\) | ||||
0.627969 | + | 0.778238i | \(0.283886\pi\) | |||||||
\(662\) | −9.75660 | −0.379201 | ||||||||
\(663\) | 45.5272 | 1.76813 | ||||||||
\(664\) | −7.19204 | −0.279105 | ||||||||
\(665\) | 6.42752 | 0.249248 | ||||||||
\(666\) | −13.7888 | −0.534307 | ||||||||
\(667\) | −45.1568 | −1.74848 | ||||||||
\(668\) | 6.20304 | 0.240003 | ||||||||
\(669\) | −29.7357 | −1.14965 | ||||||||
\(670\) | −10.8106 | −0.417650 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 1.32077 | 0.0509497 | ||||||||
\(673\) | 7.77486 | 0.299699 | 0.149849 | − | 0.988709i | \(-0.452121\pi\) | ||||
0.149849 | + | 0.988709i | \(0.452121\pi\) | |||||||
\(674\) | 10.1462 | 0.390817 | ||||||||
\(675\) | 5.62062 | 0.216338 | ||||||||
\(676\) | 15.5748 | 0.599029 | ||||||||
\(677\) | 11.1286 | 0.427708 | 0.213854 | − | 0.976866i | \(-0.431398\pi\) | ||||
0.213854 | + | 0.976866i | \(0.431398\pi\) | |||||||
\(678\) | 26.6101 | 1.02195 | ||||||||
\(679\) | 0.548361 | 0.0210442 | ||||||||
\(680\) | −6.44843 | −0.247286 | ||||||||
\(681\) | 14.3960 | 0.551654 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.91240 | −0.264496 | −0.132248 | − | 0.991217i | \(-0.542219\pi\) | ||||
−0.132248 | + | 0.991217i | \(0.542219\pi\) | |||||||
\(684\) | 8.07024 | 0.308573 | ||||||||
\(685\) | 5.46086 | 0.208649 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 4.19270 | 0.159962 | ||||||||
\(688\) | −2.71912 | −0.103665 | ||||||||
\(689\) | −45.9250 | −1.74960 | ||||||||
\(690\) | −7.27763 | −0.277055 | ||||||||
\(691\) | 31.3199 | 1.19146 | 0.595732 | − | 0.803183i | \(-0.296862\pi\) | ||||
0.595732 | + | 0.803183i | \(0.296862\pi\) | |||||||
\(692\) | −7.35006 | −0.279407 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −21.1756 | −0.803815 | ||||||||
\(695\) | −5.25491 | −0.199330 | ||||||||
\(696\) | 10.8239 | 0.410280 | ||||||||
\(697\) | −13.4353 | −0.508899 | ||||||||
\(698\) | −4.58943 | −0.173713 | ||||||||
\(699\) | 33.8543 | 1.28049 | ||||||||
\(700\) | −1.00000 | −0.0377964 | ||||||||
\(701\) | −12.1542 | −0.459058 | −0.229529 | − | 0.973302i | \(-0.573719\pi\) | ||||
−0.229529 | + | 0.973302i | \(0.573719\pi\) | |||||||
\(702\) | 30.0452 | 1.13398 | ||||||||
\(703\) | −70.5875 | −2.66226 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.75520 | −0.216753 | ||||||||
\(706\) | 32.2094 | 1.21222 | ||||||||
\(707\) | −2.44229 | −0.0918518 | ||||||||
\(708\) | 7.19364 | 0.270354 | ||||||||
\(709\) | −32.3970 | −1.21669 | −0.608347 | − | 0.793671i | \(-0.708167\pi\) | ||||
−0.608347 | + | 0.793671i | \(0.708167\pi\) | |||||||
\(710\) | −11.8156 | −0.443432 | ||||||||
\(711\) | 9.23927 | 0.346500 | ||||||||
\(712\) | −5.39995 | −0.202372 | ||||||||
\(713\) | 9.77825 | 0.366199 | ||||||||
\(714\) | −8.51686 | −0.318736 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.40431 | −0.164597 | ||||||||
\(717\) | 23.2012 | 0.866463 | ||||||||
\(718\) | −6.54031 | −0.244082 | ||||||||
\(719\) | 12.3255 | 0.459663 | 0.229832 | − | 0.973230i | \(-0.426182\pi\) | ||||
0.229832 | + | 0.973230i | \(0.426182\pi\) | |||||||
\(720\) | −1.25558 | −0.0467926 | ||||||||
\(721\) | −0.630289 | −0.0234732 | ||||||||
\(722\) | 22.3130 | 0.830403 | ||||||||
\(723\) | −7.43839 | −0.276637 | ||||||||
\(724\) | −11.0910 | −0.412193 | ||||||||
\(725\) | −8.19519 | −0.304362 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.42914 | 0.0900918 | 0.0450459 | − | 0.998985i | \(-0.485657\pi\) | ||||
0.0450459 | + | 0.998985i | \(0.485657\pi\) | |||||||
\(728\) | −5.34554 | −0.198119 | ||||||||
\(729\) | 26.8620 | 0.994888 | ||||||||
\(730\) | −5.54852 | −0.205360 | ||||||||
\(731\) | 17.5340 | 0.648519 | ||||||||
\(732\) | −17.6966 | −0.654085 | ||||||||
\(733\) | 46.1729 | 1.70543 | 0.852717 | − | 0.522373i | \(-0.174953\pi\) | ||||
0.852717 | + | 0.522373i | \(0.174953\pi\) | |||||||
\(734\) | −2.98556 | −0.110199 | ||||||||
\(735\) | −1.32077 | −0.0487172 | ||||||||
\(736\) | 5.51016 | 0.203107 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −2.61600 | −0.0962963 | ||||||||
\(739\) | 48.8700 | 1.79771 | 0.898856 | − | 0.438244i | \(-0.144399\pi\) | ||||
0.898856 | + | 0.438244i | \(0.144399\pi\) | |||||||
\(740\) | 10.9821 | 0.403709 | ||||||||
\(741\) | 45.3796 | 1.66706 | ||||||||
\(742\) | 8.59127 | 0.315395 | ||||||||
\(743\) | 19.7114 | 0.723141 | 0.361571 | − | 0.932345i | \(-0.382241\pi\) | ||||
0.361571 | + | 0.932345i | \(0.382241\pi\) | |||||||
\(744\) | −2.34381 | −0.0859284 | ||||||||
\(745\) | 9.21250 | 0.337520 | ||||||||
\(746\) | −16.8471 | −0.616817 | ||||||||
\(747\) | 9.03015 | 0.330396 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.4352 | −0.417835 | ||||||||
\(750\) | −1.32077 | −0.0482276 | ||||||||
\(751\) | −52.1667 | −1.90359 | −0.951795 | − | 0.306735i | \(-0.900763\pi\) | ||||
−0.951795 | + | 0.306735i | \(0.900763\pi\) | |||||||
\(752\) | 4.35747 | 0.158901 | ||||||||
\(753\) | −18.8979 | −0.688677 | ||||||||
\(754\) | −43.8077 | −1.59538 | ||||||||
\(755\) | 14.2773 | 0.519605 | ||||||||
\(756\) | −5.62062 | −0.204420 | ||||||||
\(757\) | −32.7016 | −1.18856 | −0.594280 | − | 0.804258i | \(-0.702563\pi\) | ||||
−0.594280 | + | 0.804258i | \(0.702563\pi\) | |||||||
\(758\) | −27.4781 | −0.998049 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.42752 | −0.233151 | ||||||||
\(761\) | 24.3007 | 0.880899 | 0.440450 | − | 0.897777i | \(-0.354819\pi\) | ||||
0.440450 | + | 0.897777i | \(0.354819\pi\) | |||||||
\(762\) | 14.5297 | 0.526357 | ||||||||
\(763\) | 8.31582 | 0.301053 | ||||||||
\(764\) | −14.3562 | −0.519388 | ||||||||
\(765\) | 8.09650 | 0.292729 | ||||||||
\(766\) | −31.3930 | −1.13428 | ||||||||
\(767\) | −29.1148 | −1.05128 | ||||||||
\(768\) | −1.32077 | −0.0476590 | ||||||||
\(769\) | 34.3945 | 1.24030 | 0.620148 | − | 0.784485i | \(-0.287073\pi\) | ||||
0.620148 | + | 0.784485i | \(0.287073\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.1606 | 0.365924 | ||||||||
\(772\) | 8.48187 | 0.305269 | ||||||||
\(773\) | 11.7248 | 0.421712 | 0.210856 | − | 0.977517i | \(-0.432375\pi\) | ||||
0.210856 | + | 0.977517i | \(0.432375\pi\) | |||||||
\(774\) | 3.41406 | 0.122716 | ||||||||
\(775\) | 1.77459 | 0.0637451 | ||||||||
\(776\) | −0.548361 | −0.0196850 | ||||||||
\(777\) | 14.5048 | 0.520355 | ||||||||
\(778\) | −0.115199 | −0.00413007 | ||||||||
\(779\) | −13.3918 | −0.479810 | ||||||||
\(780\) | −7.06020 | −0.252796 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −35.5318 | −1.27062 | ||||||||
\(783\) | −46.0621 | −1.64612 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 14.9439 | 0.533369 | ||||||||
\(786\) | 24.1671 | 0.862011 | ||||||||
\(787\) | 11.1529 | 0.397558 | 0.198779 | − | 0.980044i | \(-0.436302\pi\) | ||||
0.198779 | + | 0.980044i | \(0.436302\pi\) | |||||||
\(788\) | −4.97357 | −0.177176 | ||||||||
\(789\) | 9.00251 | 0.320498 | ||||||||
\(790\) | −7.35859 | −0.261807 | ||||||||
\(791\) | 20.1474 | 0.716360 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 71.6234 | 2.54342 | ||||||||
\(794\) | −18.2744 | −0.648534 | ||||||||
\(795\) | 11.3471 | 0.402439 | ||||||||
\(796\) | −22.6336 | −0.802227 | ||||||||
\(797\) | −14.0990 | −0.499411 | −0.249706 | − | 0.968322i | \(-0.580334\pi\) | ||||
−0.249706 | + | 0.968322i | \(0.580334\pi\) | |||||||
\(798\) | −8.48925 | −0.300516 | ||||||||
\(799\) | −28.0988 | −0.994065 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 6.78005 | 0.239561 | ||||||||
\(802\) | 30.0646 | 1.06162 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 14.2783 | 0.503556 | ||||||||
\(805\) | −5.51016 | −0.194208 | ||||||||
\(806\) | 9.48612 | 0.334134 | ||||||||
\(807\) | −5.01655 | −0.176591 | ||||||||
\(808\) | 2.44229 | 0.0859195 | ||||||||
\(809\) | 44.7742 | 1.57418 | 0.787088 | − | 0.616840i | \(-0.211588\pi\) | ||||
0.787088 | + | 0.616840i | \(0.211588\pi\) | |||||||
\(810\) | −3.65680 | −0.128487 | ||||||||
\(811\) | 33.4692 | 1.17526 | 0.587631 | − | 0.809129i | \(-0.300061\pi\) | ||||
0.587631 | + | 0.809129i | \(0.300061\pi\) | |||||||
\(812\) | 8.19519 | 0.287595 | ||||||||
\(813\) | −3.10917 | −0.109043 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16.7682 | 0.587366 | ||||||||
\(816\) | 8.51686 | 0.298150 | ||||||||
\(817\) | 17.4772 | 0.611448 | ||||||||
\(818\) | 29.2637 | 1.02318 | ||||||||
\(819\) | 6.71173 | 0.234527 | ||||||||
\(820\) | 2.08350 | 0.0727591 | ||||||||
\(821\) | −44.5883 | −1.55614 | −0.778072 | − | 0.628175i | \(-0.783802\pi\) | ||||
−0.778072 | + | 0.628175i | \(0.783802\pi\) | |||||||
\(822\) | −7.21252 | −0.251565 | ||||||||
\(823\) | −41.0470 | −1.43081 | −0.715405 | − | 0.698710i | \(-0.753758\pi\) | ||||
−0.715405 | + | 0.698710i | \(0.753758\pi\) | |||||||
\(824\) | 0.630289 | 0.0219571 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.44657 | 0.189510 | ||||||||
\(827\) | 34.2851 | 1.19221 | 0.596105 | − | 0.802907i | \(-0.296714\pi\) | ||||
0.596105 | + | 0.802907i | \(0.296714\pi\) | |||||||
\(828\) | −6.91843 | −0.240432 | ||||||||
\(829\) | 15.5238 | 0.539162 | 0.269581 | − | 0.962978i | \(-0.413115\pi\) | ||||
0.269581 | + | 0.962978i | \(0.413115\pi\) | |||||||
\(830\) | −7.19204 | −0.249639 | ||||||||
\(831\) | 23.0354 | 0.799089 | ||||||||
\(832\) | 5.34554 | 0.185323 | ||||||||
\(833\) | −6.44843 | −0.223425 | ||||||||
\(834\) | 6.94051 | 0.240330 | ||||||||
\(835\) | 6.20304 | 0.214665 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.97428 | 0.344762 | ||||||||
\(838\) | −17.3655 | −0.599883 | ||||||||
\(839\) | 12.0295 | 0.415304 | 0.207652 | − | 0.978203i | \(-0.433418\pi\) | ||||
0.207652 | + | 0.978203i | \(0.433418\pi\) | |||||||
\(840\) | 1.32077 | 0.0455708 | ||||||||
\(841\) | 38.1611 | 1.31590 | ||||||||
\(842\) | 8.29303 | 0.285797 | ||||||||
\(843\) | 29.8903 | 1.02948 | ||||||||
\(844\) | −3.78425 | −0.130259 | ||||||||
\(845\) | 15.5748 | 0.535788 | ||||||||
\(846\) | −5.47114 | −0.188102 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −8.59127 | −0.295025 | ||||||||
\(849\) | 35.7394 | 1.22657 | ||||||||
\(850\) | −6.44843 | −0.221179 | ||||||||
\(851\) | 60.5130 | 2.07436 | ||||||||
\(852\) | 15.6056 | 0.534641 | ||||||||
\(853\) | −35.5225 | −1.21627 | −0.608134 | − | 0.793834i | \(-0.708082\pi\) | ||||
−0.608134 | + | 0.793834i | \(0.708082\pi\) | |||||||
\(854\) | −13.3987 | −0.458495 | ||||||||
\(855\) | 8.07024 | 0.275996 | ||||||||
\(856\) | 11.4352 | 0.390849 | ||||||||
\(857\) | −48.4891 | −1.65636 | −0.828178 | − | 0.560465i | \(-0.810622\pi\) | ||||
−0.828178 | + | 0.560465i | \(0.810622\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.93679 | −0.0660823 | −0.0330411 | − | 0.999454i | \(-0.510519\pi\) | ||||
−0.0330411 | + | 0.999454i | \(0.510519\pi\) | |||||||
\(860\) | −2.71912 | −0.0927211 | ||||||||
\(861\) | 2.75182 | 0.0937818 | ||||||||
\(862\) | 13.3393 | 0.454338 | ||||||||
\(863\) | 21.2807 | 0.724405 | 0.362202 | − | 0.932099i | \(-0.382025\pi\) | ||||
0.362202 | + | 0.932099i | \(0.382025\pi\) | |||||||
\(864\) | 5.62062 | 0.191217 | ||||||||
\(865\) | −7.35006 | −0.249910 | ||||||||
\(866\) | −14.8300 | −0.503944 | ||||||||
\(867\) | −32.4674 | −1.10265 | ||||||||
\(868\) | −1.77459 | −0.0602334 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 10.8239 | 0.366966 | ||||||||
\(871\) | −57.7885 | −1.95809 | ||||||||
\(872\) | −8.31582 | −0.281609 | ||||||||
\(873\) | 0.688510 | 0.0233025 | ||||||||
\(874\) | −35.4166 | −1.19799 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 7.32830 | 0.247600 | ||||||||
\(877\) | 28.4478 | 0.960614 | 0.480307 | − | 0.877100i | \(-0.340525\pi\) | ||||
0.480307 | + | 0.877100i | \(0.340525\pi\) | |||||||
\(878\) | −6.08156 | −0.205243 | ||||||||
\(879\) | 26.6739 | 0.899689 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19.2969 | −0.650127 | −0.325064 | − | 0.945692i | \(-0.605386\pi\) | ||||
−0.325064 | + | 0.945692i | \(0.605386\pi\) | |||||||
\(882\) | −1.25558 | −0.0422775 | ||||||||
\(883\) | 0.696897 | 0.0234524 | 0.0117262 | − | 0.999931i | \(-0.496267\pi\) | ||||
0.0117262 | + | 0.999931i | \(0.496267\pi\) | |||||||
\(884\) | −34.4703 | −1.15936 | ||||||||
\(885\) | 7.19364 | 0.241812 | ||||||||
\(886\) | −19.8590 | −0.667176 | ||||||||
\(887\) | 10.1179 | 0.339727 | 0.169864 | − | 0.985468i | \(-0.445667\pi\) | ||||
0.169864 | + | 0.985468i | \(0.445667\pi\) | |||||||
\(888\) | −14.5048 | −0.486748 | ||||||||
\(889\) | 11.0010 | 0.368961 | ||||||||
\(890\) | −5.39995 | −0.181007 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 22.5140 | 0.753824 | ||||||||
\(893\) | −28.0077 | −0.937243 | ||||||||
\(894\) | −12.1676 | −0.406944 | ||||||||
\(895\) | −4.40431 | −0.147220 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −38.9028 | −1.29893 | ||||||||
\(898\) | 0.806539 | 0.0269145 | ||||||||
\(899\) | −14.5431 | −0.485039 | ||||||||
\(900\) | −1.25558 | −0.0418526 | ||||||||
\(901\) | 55.4002 | 1.84565 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.59132 | −0.119511 | ||||||||
\(904\) | −20.1474 | −0.670094 | ||||||||
\(905\) | −11.0910 | −0.368677 | ||||||||
\(906\) | −18.8570 | −0.626482 | ||||||||
\(907\) | −26.1814 | −0.869341 | −0.434670 | − | 0.900590i | \(-0.643135\pi\) | ||||
−0.434670 | + | 0.900590i | \(0.643135\pi\) | |||||||
\(908\) | −10.8997 | −0.361719 | ||||||||
\(909\) | −3.06648 | −0.101709 | ||||||||
\(910\) | −5.34554 | −0.177203 | ||||||||
\(911\) | −34.0567 | −1.12835 | −0.564175 | − | 0.825655i | \(-0.690806\pi\) | ||||
−0.564175 | + | 0.825655i | \(0.690806\pi\) | |||||||
\(912\) | 8.48925 | 0.281107 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −29.9349 | −0.990160 | ||||||||
\(915\) | −17.6966 | −0.585031 | ||||||||
\(916\) | −3.17445 | −0.104887 | ||||||||
\(917\) | 18.2978 | 0.604246 | ||||||||
\(918\) | −36.2442 | −1.19624 | ||||||||
\(919\) | 37.6890 | 1.24325 | 0.621623 | − | 0.783316i | \(-0.286473\pi\) | ||||
0.621623 | + | 0.783316i | \(0.286473\pi\) | |||||||
\(920\) | 5.51016 | 0.181664 | ||||||||
\(921\) | −32.2436 | −1.06246 | ||||||||
\(922\) | 33.4831 | 1.10271 | ||||||||
\(923\) | −63.1607 | −2.07896 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.9821 | 0.361089 | ||||||||
\(926\) | −29.7511 | −0.977680 | ||||||||
\(927\) | −0.791376 | −0.0259922 | ||||||||
\(928\) | −8.19519 | −0.269020 | ||||||||
\(929\) | 24.5323 | 0.804879 | 0.402440 | − | 0.915446i | \(-0.368162\pi\) | ||||
0.402440 | + | 0.915446i | \(0.368162\pi\) | |||||||
\(930\) | −2.34381 | −0.0768567 | ||||||||
\(931\) | −6.42752 | −0.210653 | ||||||||
\(932\) | −25.6323 | −0.839614 | ||||||||
\(933\) | −33.3714 | −1.09253 | ||||||||
\(934\) | −6.65053 | −0.217612 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −6.71173 | −0.219380 | ||||||||
\(937\) | 30.8744 | 1.00862 | 0.504311 | − | 0.863522i | \(-0.331746\pi\) | ||||
0.504311 | + | 0.863522i | \(0.331746\pi\) | |||||||
\(938\) | 10.8106 | 0.352979 | ||||||||
\(939\) | 24.0045 | 0.783358 | ||||||||
\(940\) | 4.35747 | 0.142125 | ||||||||
\(941\) | −46.4060 | −1.51279 | −0.756396 | − | 0.654114i | \(-0.773042\pi\) | ||||
−0.756396 | + | 0.654114i | \(0.773042\pi\) | |||||||
\(942\) | −19.7373 | −0.643078 | ||||||||
\(943\) | 11.4804 | 0.373854 | ||||||||
\(944\) | −5.44657 | −0.177271 | ||||||||
\(945\) | −5.62062 | −0.182839 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.46285 | 0.275006 | 0.137503 | − | 0.990501i | \(-0.456092\pi\) | ||||
0.137503 | + | 0.990501i | \(0.456092\pi\) | |||||||
\(948\) | 9.71897 | 0.315658 | ||||||||
\(949\) | −29.6598 | −0.962798 | ||||||||
\(950\) | −6.42752 | −0.208536 | ||||||||
\(951\) | −14.0977 | −0.457150 | ||||||||
\(952\) | 6.44843 | 0.208995 | ||||||||
\(953\) | 21.1245 | 0.684289 | 0.342145 | − | 0.939647i | \(-0.388847\pi\) | ||||
0.342145 | + | 0.939647i | \(0.388847\pi\) | |||||||
\(954\) | 10.7870 | 0.349242 | ||||||||
\(955\) | −14.3562 | −0.464555 | ||||||||
\(956\) | −17.5664 | −0.568139 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −17.9277 | −0.579217 | ||||||||
\(959\) | −5.46086 | −0.176340 | ||||||||
\(960\) | −1.32077 | −0.0426275 | ||||||||
\(961\) | −27.8508 | −0.898414 | ||||||||
\(962\) | 58.7051 | 1.89273 | ||||||||
\(963\) | −14.3578 | −0.462674 | ||||||||
\(964\) | 5.63187 | 0.181390 | ||||||||
\(965\) | 8.48187 | 0.273041 | ||||||||
\(966\) | 7.27763 | 0.234154 | ||||||||
\(967\) | −5.05793 | −0.162652 | −0.0813260 | − | 0.996688i | \(-0.525915\pi\) | ||||
−0.0813260 | + | 0.996688i | \(0.525915\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −54.7423 | −1.75858 | ||||||||
\(970\) | −0.548361 | −0.0176068 | ||||||||
\(971\) | 14.8010 | 0.474988 | 0.237494 | − | 0.971389i | \(-0.423674\pi\) | ||||
0.237494 | + | 0.971389i | \(0.423674\pi\) | |||||||
\(972\) | −12.0321 | −0.385930 | ||||||||
\(973\) | 5.25491 | 0.168465 | ||||||||
\(974\) | 37.2239 | 1.19273 | ||||||||
\(975\) | −7.06020 | −0.226107 | ||||||||
\(976\) | 13.3987 | 0.428883 | ||||||||
\(977\) | −7.38146 | −0.236154 | −0.118077 | − | 0.993004i | \(-0.537673\pi\) | ||||
−0.118077 | + | 0.993004i | \(0.537673\pi\) | |||||||
\(978\) | −22.1469 | −0.708180 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | 10.4412 | 0.333360 | ||||||||
\(982\) | −21.7165 | −0.693001 | ||||||||
\(983\) | 1.45695 | 0.0464694 | 0.0232347 | − | 0.999730i | \(-0.492603\pi\) | ||||
0.0232347 | + | 0.999730i | \(0.492603\pi\) | |||||||
\(984\) | −2.75182 | −0.0877249 | ||||||||
\(985\) | −4.97357 | −0.158471 | ||||||||
\(986\) | 52.8461 | 1.68296 | ||||||||
\(987\) | 5.75520 | 0.183190 | ||||||||
\(988\) | −34.3585 | −1.09309 | ||||||||
\(989\) | −14.9828 | −0.476424 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 34.1561 | 1.08501 | 0.542503 | − | 0.840054i | \(-0.317477\pi\) | ||||
0.542503 | + | 0.840054i | \(0.317477\pi\) | |||||||
\(992\) | 1.77459 | 0.0563432 | ||||||||
\(993\) | 12.8862 | 0.408931 | ||||||||
\(994\) | 11.8156 | 0.374768 | ||||||||
\(995\) | −22.6336 | −0.717534 | ||||||||
\(996\) | 9.49900 | 0.300987 | ||||||||
\(997\) | −56.9485 | −1.80358 | −0.901789 | − | 0.432177i | \(-0.857746\pi\) | ||||
−0.901789 | + | 0.432177i | \(0.857746\pi\) | |||||||
\(998\) | −15.7823 | −0.499582 | ||||||||
\(999\) | 61.7261 | 1.95293 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8470.2.a.db.1.2 | 6 | ||
11.3 | even | 5 | 770.2.n.g.141.3 | yes | 12 | ||
11.4 | even | 5 | 770.2.n.g.71.3 | ✓ | 12 | ||
11.10 | odd | 2 | 8470.2.a.cv.1.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.n.g.71.3 | ✓ | 12 | 11.4 | even | 5 | ||
770.2.n.g.141.3 | yes | 12 | 11.3 | even | 5 | ||
8470.2.a.cv.1.2 | 6 | 11.10 | odd | 2 | |||
8470.2.a.db.1.2 | 6 | 1.1 | even | 1 | trivial |